I have the following configuration being hosted in Azure virtual servers.

Web Server 1 and 2 located in Data Center A and Web Server 3 located in Data Center B. Each server is hosting the same sites, but duplicated from the other servers.

When traffic comes in from the internet I want it to balance the traffic across all web servers. If Web Server 1 goes down or has issues with one web site I want it to shift all sites to Web Server 2 and or 3. If there is an issue with one site on Web Server 2 I want it to shift the load to Web Server 3 fully for all sites.

1 Answer
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As mentioned by Batistuta, In Azure we can use Traffic Manager to distribute traffic to the available web site.
And traffic manager supports Priority traffic-routing method, Often an organization wants to provide reliability for its services by deploying one or more backup services in case their primary service goes down. The 'Priority' traffic-routing method allows Azure customers to easily implement this failover pattern.
More information about traffic manager, refer to the link.